MOAB: Mesh Oriented datABase  (version 5.2.1)
MBMesquite::TShapeSizeB1 Class Reference

#include <TShapeSizeB1.hpp>

+ Inheritance diagram for MBMesquite::TShapeSizeB1:
+ Collaboration diagram for MBMesquite::TShapeSizeB1:

Public Member Functions

virtual MESQUITE_EXPORT ~TShapeSizeB1 ()
virtual MESQUITE_EXPORT std::string get_name () const
virtual MESQUITE_EXPORT bool evaluate (const MsqMatrix< 2, 2 > &T, double &result, MsqError &err)
 Evaluate \(\mu(T)\).
virtual MESQUITE_EXPORT bool evaluate_with_grad (const MsqMatrix< 2, 2 > &T, double &result, MsqMatrix< 2, 2 > &deriv_wrt_T, MsqError &err)
 Gradient of \(\mu(T)\) with respect to components of T.
virtual MESQUITE_EXPORT bool evaluate_with_hess (const MsqMatrix< 2, 2 > &T, double &result, MsqMatrix< 2, 2 > &deriv_wrt_T, MsqMatrix< 2, 2 > second_wrt_T[3], MsqError &err)
 Hessian of \(\mu(T)\) with respect to components of T.
virtual MESQUITE_EXPORT bool evaluate (const MsqMatrix< 3, 3 > &T, double &result, MsqError &err)
 Evaluate \(\mu(T)\).
virtual MESQUITE_EXPORT bool evaluate_with_grad (const MsqMatrix< 3, 3 > &T, double &result, MsqMatrix< 3, 3 > &deriv_wrt_T, MsqError &err)
 Gradient of \(\mu(T)\) with respect to components of T.
virtual MESQUITE_EXPORT bool evaluate_with_hess (const MsqMatrix< 3, 3 > &T, double &result, MsqMatrix< 3, 3 > &deriv_wrt_T, MsqMatrix< 3, 3 > second_wrt_T[6], MsqError &err)
 Hessian of \(\mu(T)\) with respect to components of T.

Detailed Description

|T - T^-t|^2

Definition at line 42 of file TShapeSizeB1.hpp.


Constructor & Destructor Documentation

Definition at line 45 of file TShapeSizeB1.cpp.

{}

Member Function Documentation

bool MBMesquite::TShapeSizeB1::evaluate ( const MsqMatrix< 2, 2 > &  T,
double &  result,
MsqError err 
) [virtual]

Evaluate \(\mu(T)\).

Parameters:
T2x2 relative measure matrix (typically A W^-1)
resultOutput: value of function
Returns:
false if function cannot be evaluated for given T (e.g. division by zero, etc.), true otherwise.

Reimplemented from MBMesquite::TMetric.

Definition at line 47 of file TShapeSizeB1.cpp.

References MBMesquite::det(), MBMesquite::TMetricBarrier::invalid_determinant(), and MBMesquite::sqr_Frobenius().

{
    const double tau = det( T );
    if( invalid_determinant( tau ) )
    {  // barrier
        return false;
    }

    const double nT = sqr_Frobenius( T );
    const double f  = 1 / ( tau * tau );
    result          = ( 1 + f ) * nT - 4;
    return true;
}
bool MBMesquite::TShapeSizeB1::evaluate ( const MsqMatrix< 3, 3 > &  T,
double &  result,
MsqError err 
) [virtual]

Evaluate \(\mu(T)\).

Parameters:
T3x3 relative measure matrix (typically A W^-1)
resultOutput: value of function
Returns:
false if function cannot be evaluated for given T (e.g. division by zero, etc.), true otherwise.

Reimplemented from MBMesquite::TMetric.

Definition at line 61 of file TShapeSizeB1.cpp.

References MBMesquite::det(), MBMesquite::TMetricBarrier::invalid_determinant(), MBMesquite::sqr_Frobenius(), and MBMesquite::transpose_adj().

{
    const double tau = det( T );
    if( invalid_determinant( tau ) )
    {  // barrier
        return false;
    }

    const double nT   = sqr_Frobenius( T );
    const double nadj = sqr_Frobenius( transpose_adj( T ) );
    const double f    = 1 / ( tau * tau );
    result            = nT + f * nadj - 6;
    return true;
}
bool MBMesquite::TShapeSizeB1::evaluate_with_grad ( const MsqMatrix< 2, 2 > &  T,
double &  result,
MsqMatrix< 2, 2 > &  deriv_wrt_T,
MsqError err 
) [virtual]

Gradient of \(\mu(T)\) with respect to components of T.

Parameters:
T2x2 relative measure matrix (typically A W^-1)
resultOutput: value of function
deriv_wrt_TOutput: partial deriviatve of \(\mu\) wrt each term of T, evaluated at passed T.

\[\left[\begin{array}{cc} \frac{\partial\mu}{\partial T_{0,0}} & \frac{\partial\mu}{\partial T_{0,1}} \\ \frac{\partial\mu}{\partial T_{1,0}} & \frac{\partial\mu}{\partial T_{1,1}} \\ \end{array}\right]\]

Returns:
false if function cannot be evaluated for given T (e.g. division by zero, etc.), true otherwise.

Reimplemented from MBMesquite::TMetric.

Definition at line 76 of file TShapeSizeB1.cpp.

References MBMesquite::MsqError::BARRIER_VIOLATED, MBMesquite::barrier_violated_msg, MBMesquite::det(), MBMesquite::TMetricBarrier::invalid_determinant(), MSQ_SETERR, MBMesquite::sqr_Frobenius(), T, and MBMesquite::transpose_adj().

{
    const double tau = det( T );
    if( invalid_determinant( tau ) )
    {  // barrier
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }

    const MsqMatrix< 2, 2 > adjt = transpose_adj( T );
    const double nT              = sqr_Frobenius( T );
    const double f               = 1 / ( tau * tau );
    result                       = ( 1 + f ) * nT - 4;

    deriv_wrt_T = T;
    deriv_wrt_T *= 2 + 2 * f;
    deriv_wrt_T -= 2 * f / tau * nT * adjt;

    return true;
}
bool MBMesquite::TShapeSizeB1::evaluate_with_grad ( const MsqMatrix< 3, 3 > &  T,
double &  result,
MsqMatrix< 3, 3 > &  deriv_wrt_T,
MsqError err 
) [virtual]

Gradient of \(\mu(T)\) with respect to components of T.

Parameters:
T3x3 relative measure matrix (typically A W^-1)
resultOutput: value of function
deriv_wrt_TOutput: partial deriviatve of \(\mu\) wrt each term of T, evaluated at passed T.

\[\left[\begin{array}{ccc} \frac{\partial\mu}{\partial T_{0,0}} & \frac{\partial\mu}{\partial T_{0,1}} & \frac{\partial\mu}{\partial T_{0,2}} \\ \frac{\partial\mu}{\partial T_{1,0}} & \frac{\partial\mu}{\partial T_{1,1}} & \frac{\partial\mu}{\partial T_{1,2}} \\ \frac{\partial\mu}{\partial T_{2,0}} & \frac{\partial\mu}{\partial T_{2,1}} & \frac{\partial\mu}{\partial T_{2,2}} \end{array}\right]\]

Returns:
false if function cannot be evaluated for given T (e.g. division by zero, etc.), true otherwise.

Reimplemented from MBMesquite::TMetric.

Definition at line 98 of file TShapeSizeB1.cpp.

References MBMesquite::MsqError::BARRIER_VIOLATED, MBMesquite::barrier_violated_msg, MBMesquite::det(), MBMesquite::TMetricBarrier::invalid_determinant(), MSQ_SETERR, MBMesquite::sqr_Frobenius(), T, MBMesquite::transpose(), and MBMesquite::transpose_adj().

{
    const double tau = det( T );
    if( invalid_determinant( tau ) )
    {  // barrier
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }

    const MsqMatrix< 3, 3 > adjt = transpose_adj( T );
    const double nT              = sqr_Frobenius( T );
    const double nadj            = sqr_Frobenius( adjt );
    const double f               = 1 / ( tau * tau );
    result                       = nT + f * nadj - 6;

    deriv_wrt_T = T;
    deriv_wrt_T *= ( 1 + f * nT );
    deriv_wrt_T -= f * T * transpose( T ) * T;
    deriv_wrt_T -= f / tau * nadj * adjt;
    deriv_wrt_T *= 2;

    return true;
}
bool MBMesquite::TShapeSizeB1::evaluate_with_hess ( const MsqMatrix< 2, 2 > &  T,
double &  result,
MsqMatrix< 2, 2 > &  deriv_wrt_T,
MsqMatrix< 2, 2 >  second_wrt_T[3],
MsqError err 
) [virtual]

Hessian of \(\mu(T)\) with respect to components of T.

Parameters:
T3x3 relative measure matrix (typically A W^-1)
resultOutput: value of function
deriv_wrt_TOutput: partial deriviatve of \(\mu\) wrt each term of T, evaluated at passed T.
second_wrt_TOutput: 9x9 matrix of second partial deriviatve of \(\mu\) wrt each term of T, in row-major order. The symmetric matrix is decomposed into 3x3 blocks and only the upper diagonal blocks, in row-major order, are returned.

\[\left[\begin{array}{cc|cc} \frac{\partial^{2}\mu}{\partial T_{0,0}^2} & \frac{\partial^{2}\mu}{\partial T_{0,0}\partial A_{0,1}} & \frac{\partial^{2}\mu}{\partial T_{0,0}\partial A_{1,0}} & \frac{\partial^{2}\mu}{\partial T_{0,0}\partial A_{1,1}} \\ \frac{\partial^{2}\mu}{\partial T_{0,0}\partial A_{0,1}} & \frac{\partial^{2}\mu}{\partial T_{0,1}^2} & \frac{\partial^{2}\mu}{\partial T_{0,1}\partial A_{1,0}} & \frac{\partial^{2}\mu}{\partial T_{0,1}\partial A_{1,1}} \\ \hline & & \frac{\partial^{2}\mu}{\partial T_{1,0}^2} & \frac{\partial^{2}\mu}{\partial T_{1,0}\partial A_{1,1}} \\ & & \frac{\partial^{2}\mu}{\partial T_{1,0}\partial A_{1,1}} & \frac{\partial^{2}\mu}{\partial T_{1,1}^2} \\ \end{array}\right]\]

Returns:
false if function cannot be evaluated for given T (e.g. division by zero, etc.), true otherwise.

Reimplemented from MBMesquite::TMetric.

Definition at line 123 of file TShapeSizeB1.cpp.

References MBMesquite::MsqError::BARRIER_VIOLATED, MBMesquite::barrier_violated_msg, MBMesquite::det(), MBMesquite::TMetricBarrier::invalid_determinant(), MSQ_SETERR, MBMesquite::pluseq_scaled_2nd_deriv_of_det(), MBMesquite::pluseq_scaled_I(), MBMesquite::pluseq_scaled_outer_product(), MBMesquite::set_scaled_sum_outer_product(), MBMesquite::sqr_Frobenius(), T, and MBMesquite::transpose_adj().

{
    const double tau = det( T );
    if( invalid_determinant( tau ) )
    {  // barrier
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }

    const MsqMatrix< 2, 2 > adjt = transpose_adj( T );
    const double nT              = sqr_Frobenius( T );
    const double f               = 1 / ( tau * tau );
    result                       = ( 1 + f ) * nT - 4;

    deriv_wrt_T = T;
    deriv_wrt_T *= 2 + 2 * f;
    deriv_wrt_T -= 2 * f / tau * nT * adjt;

    set_scaled_sum_outer_product( second_wrt_T, -4 * f / tau, T, adjt );
    pluseq_scaled_I( second_wrt_T, 2 + 2 * f );
    pluseq_scaled_outer_product( second_wrt_T, 6 * nT * f * f, adjt );
    pluseq_scaled_2nd_deriv_of_det( second_wrt_T, -2 * nT * f / tau );

    return true;
}
bool MBMesquite::TShapeSizeB1::evaluate_with_hess ( const MsqMatrix< 3, 3 > &  T,
double &  result,
MsqMatrix< 3, 3 > &  deriv_wrt_T,
MsqMatrix< 3, 3 >  second_wrt_T[6],
MsqError err 
) [virtual]

Hessian of \(\mu(T)\) with respect to components of T.

Parameters:
T3x3 relative measure matrix (typically A W^-1)
resultOutput: value of function
deriv_wrt_TOutput: partial deriviatve of \(\mu\) wrt each term of T, evaluated at passed T.
second_wrt_TOutput: 9x9 matrix of second partial deriviatve of \(\mu\) wrt each term of T, in row-major order. The symmetric matrix is decomposed into 3x3 blocks and only the upper diagonal blocks, in row-major order, are returned.

\[\left[\begin{array}{ccc|ccc|ccc} \frac{\partial^{2}\mu}{\partial T_{0,0}^2} & \frac{\partial^{2}\mu}{\partial T_{0,0}\partial T_{0,1}} & \frac{\partial^{2}\mu}{\partial T_{0,0}\partial T_{0,2}} & \frac{\partial^{2}\mu}{\partial T_{0,0}\partial T_{1,0}} & \frac{\partial^{2}\mu}{\partial T_{0,0}\partial T_{1,1}} & \frac{\partial^{2}\mu}{\partial T_{0,0}\partial T_{1,2}} & \frac{\partial^{2}\mu}{\partial T_{0,0}\partial T_{2,0}} & \frac{\partial^{2}\mu}{\partial T_{0,0}\partial T_{2,1}} & \frac{\partial^{2}\mu}{\partial T_{0,0}\partial T_{2,2}} \\ \frac{\partial^{2}\mu}{\partial T_{0,0}\partial T_{0,1}} & \frac{\partial^{2}\mu}{\partial T_{0,1}^2} & \frac{\partial^{2}\mu}{\partial T_{0,1}\partial T_{0,2}} & \frac{\partial^{2}\mu}{\partial T_{0,1}\partial T_{1,0}} & \frac{\partial^{2}\mu}{\partial T_{0,1}\partial T_{1,1}} & \frac{\partial^{2}\mu}{\partial T_{0,1}\partial T_{1,2}} & \frac{\partial^{2}\mu}{\partial T_{0,1}\partial T_{2,0}} & \frac{\partial^{2}\mu}{\partial T_{0,1}\partial T_{2,1}} & \frac{\partial^{2}\mu}{\partial T_{0,1}\partial T_{2,2}} \\ \frac{\partial^{2}\mu}{\partial T_{0,0}\partial T_{0,2}} & \frac{\partial^{2}\mu}{\partial T_{0,1}\partial T_{0,2}} & \frac{\partial^{2}\mu}{\partial T_{0,2}^2} & \frac{\partial^{2}\mu}{\partial T_{0,2}\partial T_{1,0}} & \frac{\partial^{2}\mu}{\partial T_{0,2}\partial T_{1,1}} & \frac{\partial^{2}\mu}{\partial T_{0,2}\partial T_{1,2}} & \frac{\partial^{2}\mu}{\partial T_{0,2}\partial T_{2,0}} & \frac{\partial^{2}\mu}{\partial T_{0,2}\partial T_{2,1}} & \frac{\partial^{2}\mu}{\partial T_{0,2}\partial T_{2,2}} \\ \hline & & & \frac{\partial^{2}\mu}{\partial T_{1,0}^2} & \frac{\partial^{2}\mu}{\partial T_{1,0}\partial T_{1,1}} & \frac{\partial^{2}\mu}{\partial T_{1,0}\partial T_{1,2}} & \frac{\partial^{2}\mu}{\partial T_{1,0}\partial T_{2,0}} & \frac{\partial^{2}\mu}{\partial T_{1,0}\partial T_{2,1}} & \frac{\partial^{2}\mu}{\partial T_{1,0}\partial T_{2,2}} \\ & & & \frac{\partial^{2}\mu}{\partial T_{1,0}\partial T_{1,1}} & \frac{\partial^{2}\mu}{\partial T_{1,1}^2} & \frac{\partial^{2}\mu}{\partial T_{1,1}\partial T_{1,2}} & \frac{\partial^{2}\mu}{\partial T_{1,1}\partial T_{2,0}} & \frac{\partial^{2}\mu}{\partial T_{1,1}\partial T_{2,1}} & \frac{\partial^{2}\mu}{\partial T_{1,1}\partial T_{2,2}} \\ & & & \frac{\partial^{2}\mu}{\partial T_{1,0}\partial T_{1,2}} & \frac{\partial^{2}\mu}{\partial T_{1,1}\partial T_{1,2}} & \frac{\partial^{2}\mu}{\partial T_{1,2}^2} & \frac{\partial^{2}\mu}{\partial T_{1,2}\partial T_{2,0}} & \frac{\partial^{2}\mu}{\partial T_{1,2}\partial T_{2,1}} & \frac{\partial^{2}\mu}{\partial T_{1,2}\partial T_{2,2}} \\ \hline & & & & & & \frac{\partial^{2}\mu}{\partial T_{2,0}^2} & \frac{\partial^{2}\mu}{\partial T_{2,0}\partial T_{2,1}} & \frac{\partial^{2}\mu}{\partial T_{2,0}\partial T_{2,2}} \\ & & & & & & \frac{\partial^{2}\mu}{\partial T_{2,0}\partial T_{2,1}} & \frac{\partial^{2}\mu}{\partial T_{2,1}^2} & \frac{\partial^{2}\mu}{\partial T_{2,1}\partial T_{2,2}} \\ & & & & & & \frac{\partial^{2}\mu}{\partial T_{2,0}\partial T_{2,2}} & \frac{\partial^{2}\mu}{\partial T_{2,1}\partial T_{2,2}} & \frac{\partial^{2}\mu}{\partial T_{2,2}^2} \\ \end{array}\right]\]

Returns:
false if function cannot be evaluated for given T (e.g. division by zero, etc.), true otherwise.

\( \frac{\partial}{\partial T} |adj T|^2 \)

Reimplemented from MBMesquite::TMetric.

Definition at line 149 of file TShapeSizeB1.cpp.

References MBMesquite::MsqError::BARRIER_VIOLATED, MBMesquite::barrier_violated_msg, MBMesquite::det(), MBMesquite::TMetricBarrier::invalid_determinant(), MSQ_SETERR, MBMesquite::pluseq_scaled_2nd_deriv_of_det(), MBMesquite::pluseq_scaled_I(), MBMesquite::pluseq_scaled_outer_product(), MBMesquite::pluseq_scaled_sum_outer_product(), MBMesquite::set_scaled_2nd_deriv_norm_sqr_adj(), MBMesquite::sqr_Frobenius(), T, MBMesquite::transpose(), and MBMesquite::transpose_adj().

{
    const double tau = det( T );
    if( invalid_determinant( tau ) )
    {  // barrier
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }

    const MsqMatrix< 3, 3 > adjt = transpose_adj( T );
    const double nT              = sqr_Frobenius( T );
    const double nadj            = sqr_Frobenius( adjt );
    const double f               = 1 / ( tau * tau );
    result                       = nT + f * nadj - 6;

    //! \f$ \frac{\partial}{\partial T} |adj T|^2 \f$
    const MsqMatrix< 3, 3 > dNadj_dT = 2 * ( nT * T - T * transpose( T ) * T );
    deriv_wrt_T                      = T;
    deriv_wrt_T -= f / tau * nadj * adjt;
    deriv_wrt_T *= 2;
    deriv_wrt_T += f * dNadj_dT;

    // calculate negative of 2nd wrt T of (|adj T|^2 / tau^2) (sec 3.2.2)
    set_scaled_2nd_deriv_norm_sqr_adj( second_wrt_T, f, T );
    pluseq_scaled_2nd_deriv_of_det( second_wrt_T, -2 * f * f * nadj * tau, T );
    pluseq_scaled_outer_product( second_wrt_T, 6 * f * f * nadj, adjt );
    pluseq_scaled_sum_outer_product( second_wrt_T, -2 * f * f * tau, adjt, dNadj_dT );
    // calculate 2nd wrt T of this metric
    pluseq_scaled_I( second_wrt_T, 2.0 );

    return true;
}
std::string MBMesquite::TShapeSizeB1::get_name ( ) const [virtual]

Reimplemented from MBMesquite::TMetricBarrier.

Definition at line 40 of file TShapeSizeB1.cpp.

{
    return "TShapeSizeB1";
}

List of all members.


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